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Debora [2.8K]
2 years ago
8

Please answerrrrr Thank you!!!!!!!!!!!!

Mathematics
1 answer:
dlinn [17]2 years ago
3 0

The correct answers are:

_________________

 " (x − 13) ° = 53 ° " ;

_________________

 " x = 66 " ;

_________________

 " m∠2 = 55° " ;

_________________

 " m∠1 = 55° " .

__________________

<u>Step-by-step explanation</u>:

Note:  The following "given values/answers" within the attached image:

Specifically:

 (x − 13)° = 72° ; and;

  x = 85° ;

_________________

   are: "incorrect"—and are "arbitrarily assigned values"

_________________

The values and expressions given in the attached image, however, are correct/do make sense; and we can use such data to solve the problem.

_________________

Let's start by finding the measure of ∠2 ;  that is: " m∠2 " :

To find m∠2:

_________________

Note that:  both: "∠2 " ; and the angle that measures "175" with the attached image:

            → both form a <u>straight line</u>—that is;

              → they are "supplementary angles" ;

              → which means they add up to "180° " ;

_________________

So:  To solve for:  "m∠2" :

_________________

→  m∠2 = 180 − (125) = 55° ,

_________________

Now; to solve for:  " m∠1 " :

_________________

Note that ∠1 and ∠2 are vertical angles: which means that they have equal measurements;  

{since: vertical angles are congruent; which means that vertical angles are equal.} ;

_________________

→  As such, m∠1 = m∠2 = 55 °.

_________________

Now, take either ∠1 or ∠2 ; (each has the same "measurement"—"55° " ;

 And combine with angle with the given measurement of 72° ;

 And combine with the angle with the "given measurement of [the expression: ["x − 13"]° ;

_________________

All three of these angles form a <u>straight line</u>—that is;

              → they are "supplementary angles" ;

              → which means they add up to "180° " ;

So, 55° + 72° + (x − 13)° = 180° ;

 Let us solve for "x" ; and for "(x − 13)" ;

_________________

55 + 72 = 127 ;

→ 127 + (x − 13) = 180 ;

Now, subtract "127" from each side of the equation:

_________________

 → 127 + (x − 13) − 127 = 180 − 127 ;

   to get:

          " (x − 13) = 53 " ; →  which is one of our answers;

 Now, to solve for "x" ; we add "13" to Each Side of the equation;

   to isolate "x" on one side of the equation; & to solve for "x" :

_________________

      x − 13 + 13 = 53 + 13 ;

to get:

_________________

      x  = 66 ;

_________________

So:  The correct answers are:

_________________

 " (x − 13) ° = 53 ° " ;

  → Double check by substituting our value of "66" for "x" :

 " (66 − 13) =? 53 ?  Yes!  ;

_________________

 " x = 66 " ;

_________________

 " m∠2 = 55° " ;

_________________

 " m∠1 = 55° " .

_________________

Hope these answers—and explanations—are helpful!

  Best wishes!

_________________

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